ANTICIPATED FUNCTION SYNCHRONIZATION WITH UNKNOWN PARAMETERS OF DISCRETE-TIME CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (04) ◽  
pp. 597-608 ◽  
Author(s):  
YIN LI ◽  
BIAO LI ◽  
YONG CHEN
Keyword(s):  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Law ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Function Synchronization

In this paper, firstly, the control problem for the chaos synchronization of discrete-time chaotic (hyperchaotic) systems with unknown parameters are considered. Next, backstepping control law is derived to make the error signals between drive 2D discrete-time chaotic system and response 2D discrete-time chaotic system with two uncertain parameters asymptotically synchronized. Finally, the approach is extended to the synchronization problem for 3D discrete-time chaotic system with two unknown parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

Adaptive Synchronization of Chaotic Genesio–Tesi Systems Via A Nonlinear Control

2018 ◽  
Vol 7 (3.19) ◽  
pp. 136
Author(s):  
Esmat Sadat Alaviyan Shahri
Keyword(s):  
Nonlinear Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Strategy ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
Control Effort ◽  
Analysis And Design ◽  
Synchronization Problem ◽  
Synchronization Scheme

The paper presents the stabilization and adaptive synchronization problem of a class of chaotic systems (Genesio–Tesi system) with three unknown parameters. A novel nonlinear control effort is proposed and an adaptive strategy is presented in order to the states of two Genesio–Tesi systems were asymptotically synchronized. The known Lyapunov method guarantees the presented stability analysis and design. An illustrative simulation result is given to demonstrate the effectiveness of the proposed chaos synchronization scheme.

scholarly journals Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

2015 ◽  
Vol 25 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Mathematical Properties ◽  
Quadratic Nonlinearities

AbstractFirst, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1= 0.0395,L2= 0 and L3= −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY=3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

Anti-Synchronization for a Modified Chen-Qi-Like Chaotic System

2012 ◽  
Vol 220-223 ◽  
pp. 2113-2116
Author(s):  
Su Hai Huang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Stability Theorem ◽  
Control Law ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Dynamical Characteristics ◽  
Control Scheme ◽  
Adaptive Control Scheme

A modified Chen-Qi-like chaotic system is presented. Some basic dynamical characteristics of this system are studied by calculating the Lyapunov exponent and phase figure. Based on the Lyapunov stability theorem, adaptive control scheme and parameters update law are presented for the anti-synchronization of new chaotic systems with fully unknown parameters. Finally, the numerical simulation verify that the control law and parameter changing are correct.

SYNCHRONIZATION CONTROL FOR A CLASS OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

2005 ◽  
Vol 15 (07) ◽  
pp. 2235-2246 ◽  
Author(s):  
HER-TERNG YAU ◽  
JUI-SHENG LIN ◽  
JUN-JUH YAN
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Sliding Mode ◽  
Variable Structure ◽  
Synchronization Control ◽  
Control Law ◽  
Structure Control ◽  
Synchronization Problem ◽  
Error State

This paper investigates the chaos synchronization problem for a class of uncertain master-slave chaotic systems. Based on the variable structure control theory, a strategy is proposed to guarantee the occurrence of a sliding mode motion of error states when the proposed control law is applied. As expected, the error state is able to drive to zero with match external uncertainties or into a predictable neighborhood of zero with mismatch external uncertainties. Furthermore, a modified continuous sliding mode controller is also proposed to avoid the chattering. Examples of Lorenz system and Chua's circuit are presented to demonstrate the obtained results.

scholarly journals FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
J. Perez-Padron ◽  
C. Posadas-Castillo ◽  
J. Paz-Perez ◽  
E. Zambrano-Serrano ◽  
M. A. Platas-Garza
Keyword(s):  
Time Delay ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Tracking Error ◽  
Control Law ◽  
Trajectory Tracking Control ◽  
Field Programmable ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicability of the approach is illustrated by considering two different chaotic systems: Liu chaotic system and Genesio–Tesi chaotic system. The numerical results have shown the effectiveness of obtained theoretical results. Finally, the theoretical results are implemented on an FPGA, confirming the feasibility of the synchronization scheme and showing that it is hardware realizable.

Synchronization of Quadratic Chaotic Systems Based on Simultaneous Estimation of Nonlinear Dynamics

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Amin Zarei ◽  
Saeed Tavakoli
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Simultaneous Estimation ◽  
Control Law ◽  
Adaptive Mechanism ◽  
Lyapunov Theorem ◽  
Unknown Parameters ◽  
The Lorenz System ◽  
Synchronization Scheme

To synchronize quadratic chaotic systems, a synchronization scheme based on simultaneous estimation of nonlinear dynamics (SEND) is presented in this paper. To estimate quadratic terms, a compensator including Jacobian matrices in the proposed master–slave schematic is considered. According to the proposed control law and Lyapunov theorem, the asymptotic convergence of synchronization error to zero is proved. To identify unknown parameters, an adaptive mechanism is also used. Finally, a number of numerical simulations are provided for the Lorenz system and a memristor-based chaotic system to verify the proposed method.

scholarly journals Circuit Implementation Synchronization between Two Modified Fractional-Order Lorenz Chaotic Systems via a Linear Resistor and Fractional-Order Capacitor in Parallel Coupling

2021 ◽  
Vol 2021 ◽  
pp. 1-8 ◽  
Author(s):  
Juan Liu ◽  
Xuefeng Cheng ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
Synchronization Scheme

In this study, a modified fractional-order Lorenz chaotic system is proposed, and the chaotic attractors are obtained. Meanwhile, we construct one electronic circuit to realize the modified fractional-order Lorenz chaotic system. Most importantly, using a linear resistor and a fractional-order capacitor in parallel coupling, we suggested one chaos synchronization scheme for this modified fractional-order Lorenz chaotic system. The electronic circuit of chaos synchronization for modified fractional-order Lorenz chaotic has been given. The simulation results verify that synchronization scheme is viable.

scholarly journals Chaos synchronization of fractional–order discrete–time systems with different dimensions using two scaling matrices

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 942-949 ◽  
Author(s):  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Amina–Aicha Khennaoui ◽  
Giuseppe Grassi ◽  
Xiong Wang ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Strategies ◽  
Response System ◽  
Discrete Time Systems ◽  
Different Dimensions ◽  
Synchronization Scheme ◽  
Time Systems

Abstract In this paper, we study the synchronization of fractional–order discrete–time chaotic systems by means of two scaling matrices Θ and Φ. The considered synchronization scheme can be tailored to encompass several types of classical synchronization types. We proposed two nonlinear control strategies for the Θ–Φ synchronization of an m–dimensional drive system and an n–dimensional response system, whereby the synchronization dimension d = m and d = n, respectively. Numerical examples are presented to test the findings of the study.

scholarly journals Synchronization of an Uncertain Duffing Oscillator with Higher Order Chaotic Systems

2018 ◽  
Vol 28 (4) ◽  
pp. 625-634 ◽  
Author(s):  
Jacek Kabziński
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Duffing Oscillator ◽  
Higher Order ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Control Techniques ◽  
Synchronization Problems

Abstract The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing-Arneodo and Duffing-Chua synchronization problems.

scholarly journals Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

2017 ◽  
Vol 7 (6) ◽  
pp. 3446 ◽  
Author(s):  
Hamed Tirandaz ◽  
Mohsen Ahmadnia ◽  
Hamid Reza Tavakoli
Keyword(s):  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Lag Synchronization ◽  
Synchronization Problem ◽  
Projective Lag Synchronization ◽  
Control And Synchronization

In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems.

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